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Please answer using the variables provided and show explanations and work spaced out. I cannot understand when its all typed together. Please circle final answers for each of the three parts.
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- A particle moves through 3-space in such a way that its acceleration is a(t)= 8sin 2ri +8cos 2tj+e'k . where t is time measured in seconds. The initial velocity of the particle is v, = 2i – 3j+k. At time t = t , find i) the velocity vector of the particle. ii) the scalar tangential and normal components of acceleration.A particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.The position vector of a particle is r(t). Find the requested vector. 1. The velocity at t = pi/4 for r(t) = 2sec2(t) i - 6tan(t) j + 4t2 k. 2. The acceleration at t = 3 for r(t) = (5t - 2t4) i + (9 - t) j + (8t2 - 9) k.
- WRITE THE ANSWER IN 10 MINUTES PLEASE ! ! ! A particle is moving in three dimensions and its position vector is given by; r(t)= (3t^2+3.5t)i + (2.5t−4.8)j+ (2.8t^3+4.5t)k where r is in meters and ?t is in seconds. Determine the magnitude of the instantaneous acceleration at t=3s. Express your answer in units of m/s2 using one decimal place.The acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at the origin at t = 0 s and has an initial velocity Vo = 2(m/s) i + 3(m/s) j. Find: a) The velocity of the particle as a function of time. b) The maximum height the particle reaches.The velocity of a particle (in meters per second) is given by v = 16t'i+ 4tj + (5t + 2)k, wheret is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant? a = 75.16 m s^-2 ;r = (36.67, 10, 8) a = 80.16 m s^-2;r = (42.67, 16, 14) a = 85.16 m s^-2;r = (48.67, 24, 20) O None of the choices
- 1. A particle is moving in the xy plane starting from the origin with an initial velocity in x of 15 meters per second and an initial velocity in y of-10 meters per second. The object moves at constant velocity in x and constant acceleration in y. The acceleration in y is -1 m/s?. (a) Determine the total velocity vector v at any time, t. (Ans.: D 151- (10+ t)j) (b) Determine the position of the particle i at any time, t. %3D (Ans.: 7 = (15t)i – (10t +t2)i) %3D (c) What is the position of the particle after 5 seconds? (Ans.: r = 97.63 m, 0 = 39.81)A particle trajectory is described by x= ( 0.7t -5. 7 t ) m, and y=(1t -4.4 t) m. where t is in seconds. red (1) what is the position of the particle at t = 4.2 s 3.0 tion (2) what is the velocity of the particle at t = 4.2 s )j m/s (3) What is the speed of the particle at t = 3 s m/s us page abus Summary Jump to...What is the instantaneous acceleration of a particle at t = 0.56 s whose position vector is given by the function 7= (2.1lt?)i + (3.6t) j. Assume all quantities are in Sl units. O ā = (0.66 m/s²)i + (2.0 m/s²)} O ā = (3.6 m/s?) Oā = (4.2 m/s²)î O ā = (2.1 m/s²)î + (3.6 m/s²)ĵ
- IT.0.0a Given an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0. a(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0) What is the velc | vector? v(t) =A particle r = (2t3+ 3t) i + (4 - 5t2) j - t4 k Position depending on time given positionmoves with the vector. Here r is in meters and t is in seconds.a) How far has it traveled at the end of the first 3 seconds?b) What is the angle between the instantaneous vector t = 2 s and the position vector?Problem 2. A particle moves in the xy plane with a constant acceleration given by à (-2î + 8j)m/s, respectively. What is the distance from the origin to the particle at t = 2.0 s? a) 6.4m b) 10m c) 8.9m d) 2.0m e) 6.2m -4ĵ m/s². At t = 0, its position and velocity are 10î m and